%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP128-1.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:31:25 PM UTC 2026
% Result : Unsatisfiable 2.16s 1.20s
% Output : CNFRefutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 77 ( 13 unt; 0 def)
% Number of atoms : 208 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 261 ( 130 ~; 131 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 85 ( 0 sgn 85 !; 0 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f4,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f5,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f7,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f10,axiom,
! [X0,X1] :
( product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f12,axiom,
! [X2,X3,X0,X1] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f13,axiom,
! [X2,X3,X0,X1] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f14,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X0,X2,X3)
| ~ product(X2,X1,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
tcf(c_63,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X0,X2,X3)
| ~ product(X2,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_70,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[],[f7]) ).
tcf(c_72,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[],[f5]) ).
tcf(c_73,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f4]) ).
tcf(c_74,plain,
group_element(e_1),
inference(cnf_transformation,[],[f1]) ).
tcf(c_75,plain,
group_element(e_3),
inference(cnf_transformation,[],[f3]) ).
tcf(c_76,plain,
group_element(e_2),
inference(cnf_transformation,[],[f2]) ).
tcf(c_78,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_73,c_65]) ).
tcf(c_140,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_139]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_73,c_64]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_72,c_65]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_72,c_64]) ).
tcf(c_172,plain,
( ~ product(e_3,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_171]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[c_70,c_65]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[c_70,c_64]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X0,X2,e_2)
| ~ product(X2,X1,e_2)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X0,e_2,X2)
| ~ product(e_2,X1,X2)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_2,X0,X2)
| ~ product(e_2,X1,X0)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X0,e_3,X2)
| ~ product(e_3,X1,X2)
| ~ product(X0,X1,e_3) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_236,plain,
( product(e_1,e_3,e_1)
| ~ product(e_3,e_1,e_1)
| ~ product(e_1,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_235]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_3,X0,X2)
| ~ product(e_3,X1,X0)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_245,plain,
! [X0: $i] :
( ~ product(e_2,X0,e_1)
| ~ product(e_1,X0,e_1) ),
inference(instantiation,[status(thm)],[c_147]) ).
tcf(c_247,plain,
! [X0: $i] :
( product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_250,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_247]) ).
tcf(c_252,plain,
! [X0: $i] :
( ~ product(e_3,X0,e_1)
| ~ product(e_2,X0,e_1) ),
inference(instantiation,[status(thm)],[c_198]) ).
tcf(c_253,plain,
! [X0: $i] :
( ~ product(e_3,X0,e_1)
| ~ product(e_1,X0,e_1) ),
inference(instantiation,[status(thm)],[c_171]) ).
tcf(c_255,plain,
! [X0: $i,X1: $i] :
( product(e_3,X0,e_2)
| ~ product(e_3,X1,X0)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_237]) ).
tcf(c_257,plain,
! [X0: $i,X1: $i] :
( product(e_2,X0,e_2)
| ~ product(e_2,X1,X0)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_233]) ).
tcf(c_258,plain,
! [X0: $i,X1: $i] :
( product(X0,e_2,e_2)
| ~ product(e_2,X1,e_2)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_230]) ).
tcf(c_262,plain,
( product(e_3,e_1,e_2)
| ~ product(e_3,e_1,e_1)
| ~ product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_255]) ).
tcf(c_267,plain,
! [X0: $i] :
( ~ product(X0,e_3,e_2)
| ~ product(X0,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_163]) ).
tcf(c_282,plain,
! [X0: $i] :
( ~ product(X0,e_3,e_2)
| ~ product(X0,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_190]) ).
tcf(c_301,plain,
! [X0: $i] :
( ~ product(e_2,X0,e_2)
| ~ product(e_1,X0,e_2) ),
inference(instantiation,[status(thm)],[c_147]) ).
tcf(c_322,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_2) ),
inference(instantiation,[status(thm)],[c_247]) ).
tcf(c_323,plain,
! [X0: $i] :
( product(X0,e_2,e_1)
| ~ product(e_2,e_3,e_1)
| ~ product(X0,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_231]) ).
tcf(c_324,plain,
( product(e_1,e_2,e_1)
| ~ product(e_2,e_3,e_1)
| ~ product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_323]) ).
tcf(c_326,plain,
( ~ product(e_3,e_3,e_1)
| ~ product(e_1,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_253]) ).
tcf(c_351,plain,
( ~ product(e_3,e_3,e_1)
| ~ product(e_2,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_252]) ).
tcf(c_352,plain,
( ~ product(e_2,e_3,e_1)
| ~ product(e_1,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_245]) ).
tcf(c_450,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,e_3,X1)
| product(X2,X0,e_2)
| product(X2,X0,e_1)
| ~ group_element(X2)
| ~ group_element(X0)
| ~ product(e_3,X0,X1) ),
inference(superposition,[status(thm)],[c_67,c_63]) ).
tcf(c_544,plain,
! [X0: $i] :
( product(e_1,e_3,X0)
| ~ product(e_1,e_3,e_3)
| ~ product(e_3,e_3,X0) ),
inference(instantiation,[status(thm)],[c_235]) ).
tcf(c_547,plain,
( product(e_1,e_3,e_1)
| ~ product(e_3,e_3,e_1)
| ~ product(e_1,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_544]) ).
tcf(c_660,plain,
! [X0: $i] :
( ~ product(e_3,X0,e_3)
| ~ product(e_2,X0,e_3) ),
inference(instantiation,[status(thm)],[c_198]) ).
tcf(c_689,plain,
! [X0: $i,X1: $i] :
( product(X0,e_3,X1)
| ~ product(e_3,e_3,X1)
| ~ product(X0,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_235]) ).
tcf(c_694,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1)
| ~ group_element(e_3) ),
inference(instantiation,[status(thm)],[c_247]) ).
tcf(c_695,plain,
( ~ product(e_3,e_3,e_3)
| ~ product(e_1,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_171]) ).
tcf(c_733,plain,
! [X0: $i] :
( product(e_2,e_3,e_2)
| ~ product(e_3,X0,e_2)
| ~ product(e_2,X0,e_3) ),
inference(instantiation,[status(thm)],[c_257]) ).
tcf(c_879,plain,
( product(e_2,e_2,e_2)
| ~ product(e_2,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_258]) ).
tcf(c_889,plain,
( ~ product(e_2,e_3,e_2)
| ~ product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_301]) ).
tcf(c_903,plain,
! [X0: $i,X1: $i] :
( product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| product(X1,e_3,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(e_3)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_67,c_450]) ).
tcf(c_904,plain,
! [X0: $i,X1: $i] :
( product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| product(X1,e_3,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_903,c_75]) ).
tcf(c_950,plain,
( ~ product(e_3,e_3,e_2)
| ~ product(e_3,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_267]) ).
tcf(c_1007,plain,
! [X0: $i] :
( product(e_3,e_3,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(equality_factoring,[status(thm)],[c_904]) ).
tcf(c_1009,plain,
! [X0: $i] :
( product(e_3,e_3,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1007,c_75]) ).
tcf(c_1165,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_1009]) ).
tcf(c_1414,plain,
! [X0: $i] :
( product(e_2,e_3,X0)
| ~ product(e_2,e_3,e_3)
| ~ product(e_3,e_3,X0) ),
inference(instantiation,[status(thm)],[c_689]) ).
tcf(c_1415,plain,
( product(e_2,e_3,e_1)
| ~ product(e_3,e_3,e_1)
| ~ product(e_2,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_1414]) ).
tcf(c_1488,plain,
( product(e_2,e_3,e_2)
| ~ product(e_3,e_3,e_2)
| ~ product(e_2,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_733]) ).
tcf(c_1590,plain,
! [X0: $i] :
( product(X0,e_1,e_1)
| ~ product(e_1,e_2,e_1)
| ~ product(X0,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_1591,plain,
( product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_1590]) ).
tcf(c_1619,plain,
( ~ product(e_2,e_3,e_2)
| ~ product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_282]) ).
tcf(c_1640,plain,
( ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_660]) ).
tcf(c_1740,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1640,c_1619,c_1591,c_1488,c_1415,c_1165,c_950,c_889,c_879,c_695,c_694,c_547,c_351,c_352,c_326,c_324,c_322,c_262,c_250,c_236,c_172,c_140,c_78,c_74,c_75,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP128-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 13:46:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running EPR theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s epr_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 2.16/1.20 % SZS status Started for theBenchmark.p
% 2.16/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 2.16/1.20
% 2.16/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.16/1.20
% 2.16/1.20 % ------ iProver source info
% 2.16/1.20
% 2.16/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 2.16/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.16/1.20 % git: non_committed_changes: false
% 2.16/1.20
% 2.16/1.20 % ------ Parsing...% successful
% 2.16/1.20
% 2.16/1.20
% 2.16/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 2.16/1.20 %
% 2.16/1.20
% 2.16/1.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e %
% 2.16/1.20
% 2.16/1.20 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 2.16/1.20 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.16/1.20 % ------ Proving...
% 2.16/1.20 % ------ Problem Properties
% 2.16/1.20
% 2.16/1.20 %
% 2.16/1.20 % clauses 14
% 2.16/1.20 % conjectures 1
% 2.16/1.20 % EPR 14
% 2.16/1.20 % Horn 13
% 2.16/1.20 % unary 3
% 2.16/1.20 % binary 9
% 2.16/1.20 % lits 29
% 2.16/1.20 % lits eq 0
% 2.16/1.20 % fd_pure 0
% 2.16/1.20 % fd_pseudo 0
% 2.16/1.20 % fd_cond 0
% 2.16/1.20 % fd_pseudo_cond 0
% 2.16/1.20 % AC symbols 0
% 2.16/1.20
% 2.16/1.20 % ------ Schedule EPR non Horn non eq is on
% 2.16/1.20
% 2.16/1.20 % ------ no equalities: superposition off
% 2.16/1.20
% 2.16/1.20 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 2.16/1.20
% 2.16/1.20
% 2.16/1.20 % ------
% 2.16/1.20 % Current options:
% 2.16/1.20 % ------
% 2.16/1.20
% 2.16/1.20
% 2.16/1.20 %
% 2.16/1.20
% 2.16/1.20 % ------ Proving...
% 2.16/1.20 %
% 2.16/1.20
% 2.16/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 2.16/1.20
% 2.16/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.16/1.20
% 2.16/1.20
%------------------------------------------------------------------------------